It seems to be a pearl of conventional wisdom that parameter learning in deep sum-product networks is surprisingly fast compared to shallow mixture models. This paper examines the effects of overparameterization in sum-product networks on the speed of parameter optimisation. Using theoretical analysis and empirical experiments, we show that deep sum-product networks exhibit an implicit acceleration compared to their shallow counterpart. In fact, gradient-based optimisation in deep tree-structured sum-product networks is equal to gradient ascend with adaptive and time-varying learning rates and additional momentum terms.

In many high-dimensional estimation problems the main task consists in minimizing a cost function, which is often strongly non-convex when scanned in the space of parameters to be estimated. A standard solution to flatten the corresponding rough landscape consists in summing the losses associated to different data points and obtain a smoother empirical risk. Here we propose a complementary method that works for a single data point. The main idea is that a large amount of the roughness is uncorrelated in different parts of the landscape. One can then substantially reduce the noise by evaluating an empirical average of the gradient obtained as a sum over many random independent positions in the space of parameters to be optimized. We present an algorithm, called Replicated Gradient Descent, based on this idea and we apply it to tensor PCA, which is a very hard estimation problem. We show that Replicated Gradient Descent over-performs physical algorithms such as gradient descent and approximate message passing and matches the best algorithmic thresholds known so far, obtained by tensor unfolding and methods based on sum-of-squares.

We propose a new class of structured methods for Monte Carlo (MC) sampling, called DPPMC, designed for high-dimensional nonisotropic distributions where samples are correlated to reduce the variance of the estimator via determinantal point processes. We successfully apply DPPMCs to problems involving nonisotropic distributions arising in guided evolution strategy (GES) methods for RL, CMA-ES techniques and trust region algorithms for blackbox optimization, improving state-of-the-art in all these settings. In particular, we show that DPPMCs drastically improve exploration profiles of the existing evolution strategy algorithms. We further confirm our results, analyzing random feature map estimators for Gaussian mixture kernels. We provide theoretical justification of our empirical results, showing a connection between DPPMCs and structured orthogonal MC methods for isotropic distributions.

Diagnosis and treatment guidance are aided by detecting relevant biomarkers in medical images. Although supervised deep learning can perform accurate segmentation of pathological areas, it is limited by requiring a-priori definitions of these regions, large-scale annotations, and a representative patient cohort in the training set. In contrast, anomaly detection is not limited to specific definitions of pathologies and allows for training on healthy samples without annotation. Anomalous regions can then serve as candidates for biomarker discovery. Knowledge about normal anatomical structure brings implicit information for detecting anomalies. We propose to take advantage of this property using bayesian deep learning, based on the assumption that epistemic uncertainties will correlate with anatomical deviations from a normal training set. A Bayesian U-Net is trained on a well-defined healthy environment using weak labels of healthy anatomy produced by existing methods. At test time, we capture epistemic uncertainty estimates of our model using Monte Carlo dropout. A novel post-processing technique is then applied to exploit these estimates and transfer their layered appearance to smooth blob-shaped segmentations of the anomalies. We experimentally validated this approach in retinal optical coherence tomography (OCT) images, using weak labels of retinal layers. Our method achieved a Dice index of 0.789 in an independent anomaly test set of age-related macular degeneration (AMD) cases. The resulting segmentations allowed very high accuracy for separating healthy and diseased cases with late wet AMD, dry geographic atrophy (GA), diabetic macular edema (DME) and retinal vein occlusion (RVO). Finally, we qualitatively observed that our approach can also detect other deviations in normal scans such as cut edge artifacts.

Stochastic variance reduced methods have gained a lot of interest recently for empirical risk minimization due to its appealing run time complexity. When the data size is large and disjointly stored on different machines, it becomes imperative to distribute the implementation of such variance reduced methods. In this paper, we consider a general framework that directly distributes popular stochastic variance reduced methods, by assigning outer loops to the parameter server, and inner loops to worker machines. This framework is natural as it does not require sampling extra data and is friendly to implement, but its theoretical convergence is not well understood. We obtain a unified understanding of the convergence for algorithms under this framework by measuring the smoothness of the discrepancy between the local and global loss functions. We establish the linear convergence of distributed versions of a family of stochastic variance reduced algorithms, including those using accelerated and recursive gradient updates, for minimizing strongly convex losses. Our theory captures how the convergence of distributed algorithms behaves as the number of machines and the size of local data vary. Furthermore, we show that when the smoothness discrepancy between local and global loss functions is large, regularization can be used to ensure convergence. Our analysis can be further extended to handle nonsmooth and nonconvex loss functions.

We provide an online convex optimization algorithm with regret that interpolates between the regret of an algorithm using an optimal preconditioning matrix and one using a diagonal preconditioning matrix. Our regret bound is never worse than that obtained by diagonal preconditioning, and in certain setting even surpasses that of algorithms with full-matrix preconditioning. Importantly, our algorithm runs in the same time and space complexity as online gradient descent. Along the way we incorporate new techniques that mildly streamline and improve logarithmic factors in prior regret analyses. We conclude by benchmarking our algorithm on synthetic data and deep learning tasks.

Achieving faster execution with shorter compilation time can enable further diversity and innovation in neural networks. However, the current paradigm of executing neural networks either relies on hand-optimized libraries, traditional compilation heuristics, or very recently, simulated annealing and genetic algorithms. Our work takes a unique approach by formulating compiler optimizations for neural networks as a reinforcement learning problem, whose solution takes fewer steps to converge. This solution, dubbed ReLeASE, comes with a sampling algorithm that leverages clustering to focus the costly samples (real hardware measurements) on representative points, subsuming an entire subspace. Our adaptive sampling not only reduces the number of samples, but also improves the quality of samples for better exploration in shorter time. As such, experimentation with real hardware shows that reinforcement learning with adaptive sampling provides 4.45x speed up in optimization time over AutoTVM, while also improving inference time of the modern deep networks by 5.6%. Further experiments also confirm that our adaptive sampling can even improve AutoTVM's simulated annealing by 4.00x.

The development of models for learning music similarity and feature extraction from audio media files is an increasingly important task for the entertainment industry. This work proposes a novel music classification model based on metric learning and feature extraction from MP3 audio files. The metric learning process considers the learning of a set of parameterized distances employing a structured prediction approach from a set of MP3 audio files containing several music genres. The main objective of this work is to make possible learning a personalized metric for each customer. To extract the acoustic information we use the Mel-Frequency Cepstral Coefficient (MFCC) and make a dimensionality reduction with the use of Principal Components Analysis. We attest the model validity performing a set of experiments and comparing the training and testing results with baseline algorithms, such as K-means and Soft Margin Linear Support Vector Machine (SVM). Experiments show promising results and encourage the future development of an online version of the learning model.

We revisit the stochastic variance-reduced policy gradient (SVRPG) method proposed by Papini et al. (2018) for reinforcement learning. We provide an improved convergence analysis of SVRPG and show that it can find an $\epsilon$-approximate stationary point of the performance function within $O(1/\epsilon^{5/3})$ trajectories. This sample complexity improves upon the best known result $O(1/\epsilon^2)$ by a factor of $O(1/\epsilon^{1/3})$. At the core of our analysis is (i) a tighter upper bound for the variance of importance sampling weights, where we prove that the variance can be controlled by the parameter distance between different policies; and (ii) a fine-grained analysis of the epoch length and batch size parameters such that we can significantly reduce the number of trajectories required in each iteration of SVRPG. We also empirically demonstrate the effectiveness of our theoretical claims of batch sizes on reinforcement learning benchmark tasks.

Complex classification performance metrics such as the F${}_\beta$-measure and Jaccard index are often used, in order to handle class-imbalanced cases such as information retrieval and image segmentation. These performance metrics are not decomposable, that is, they cannot be expressed in a per-example manner, which hinders a straightforward application of the M-estimation widely used in supervised learning. In this paper, we consider \emph{linear-fractional metrics}, which are a family of classification performance metrics that encompasses many standard metrics such as the F${}_\beta$-measure and Jaccard index, and propose methods to directly maximize performances under those metrics. A clue to tackle their direct optimization is a \emph{calibrated surrogate utility}, which is a tractable lower bound of the true utility function representing a given metric. We characterize necessary conditions which make the surrogate maximization coincide with the maximization of the true utility. To the best of our knowledge, this is the first surrogate calibration analysis for the linear-fractional metrics. We also propose gradient-based optimization algorithms and show their practical usefulness in experiments.